Method for detecting a magnetic source by measuring the magnetic field thereabout

ABSTRACT

A pair of magnetometer units symmetrically displaced from a reference measuring point along one axis and at least one magnetometer unit displaced from the reference point along a second axis perpendicular to the first axis respectively sense three and two directional field components of a magnetic source along two axes at each of the unit locations parallel to the first and second axes and a third axis perpendicular thereto at each of said pair of units. Total field strength and field gradients of the magnetic source are calculated from measurement sensor signals supplied by the magnetometer units to determine the position of the magnetic source relative to the reference point and its magnetic moments.

BACKGROUND OF THE INVENTION

This invention is concerned with a method for detecting a magneticsource by measuring the magnetic field issued therefrom.

The prior art does not provide practical means for measuring theaccurate position of a magnetic source to the extent necessary foractual usage.

SUMMARY OF THE INVENTION

It is the object of the invention to provide a method for accuratelydetecting a magnetic source by the measurement of the magnetic fieldissued therefrom.

Let it be assumed that a magnetic body or an assembly or agglomerationof magnetic substances is a point dipole when it is observed from apoint remote therefrom more than about 1.5 times of the total maximumlength of the body or the assembly. Assuming that the origin of thecoordinate axes are positioned at the center point of the magnetic body,the 3 axes (x,y,z) perpendicular to each other intersect at the originand are directed toward north-south, east-west, up and down directions,respectively. If the magnetic potentials are φx, φy, φz at a measuringpoint p(x,y,z) remote from the origin, and the magnetic moments of themagnetic body are Mx,My,Mz, the following equations can be derived bythe magnetic potentials on the basis of the potential theory. ##EQU1##

Each of the components of the field gradients may be expressed by thefollowing equations in terms of the fields of point P(x,y,z) Hx,Hy andHz. ##EQU2##

These field gradients are regulated by the following physicalmathematical laws;

Laplacian equation: ##EQU3##

Maxwell's equation: ##EQU4##

Euler's equation: ##EQU5## where n is the coefficient representing theexpansion of the magnetic source. In case the magnetic source is a pointdipole, then n=3. ##EQU6##

Total magnetic field is; ##EQU7##

According to the present invention, the total field and field gradientsare expressed by nearly equal equations which are composed of themeasuring data so as to achieve the object of this invention.

BRIEF EXPLANATIONS OF THE DRAWINGS

FIG. 1 shows a 4 point arrangement of the magnetometer sensor array bythe method of this invention;

FIG. 2 shows a modified arrangement of FIG. 1;

FIG. 3 shows one example in perspective view of an installation ofmagnetometer sensors and other related devices, in accordance with theinvention;

FIG. 4 is a block diagram showing the detection system used for carryingout the method of this invention;

FIG. 5 is a perspective view showing a 4 point arrangement of themagnetometer sensors according to this invention;

FIG. 6 shows a variation of FIG. 5. in the form of a 3 point arrangementof the magnetometer sensors; and

FIG. 7, FIG. 8 and FIG. 9 show comparison curves of the detectiondistance between the true value and the computed value which wereobtained by the method of this invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

As shown in FIG. 1, the points, A, B; C, D are arranged symmetricallywith respect to the measuring point P on the axes x,y, respectively, forlocation of two pair of magnetometer sensor units including one pair ofunits, each having three sensors detecting directional field strengthcomponents along three mutually perpendicular axes (H_(Ax), H_(Ay),H_(Az) ; H_(Bx), H_(By), H_(Bz)) at the points A and B, respectively,and the second pair of units, each having two sensors detectingdirectional field strength components along two perpendicular axes(H_(Cy), H_(Cz) ; H_(Dy), H_(Dz)) at points C and D, respectively. Let:##EQU8##

Then, the field gradients and total field at the point P are determinedby the following nearly equal equations. ##EQU9##

For measuring the magnetic field at 4 points A, B, C, D, the 3components Hx, Hy, Hz are measured at points A, and B and measure the 2components of Hy, Hz at points C and D.

Then, the total magnetic field is:

    H.sub.t =1/2{(H.sub.Ax.sup.2 +H.sub.Ay.sup.2 +H.sub.Az.sup.2).sup.1/2 +(H.sub.Bx.sup.2 +H.sub.By.sup.2 +H.sub.Bz.sup.2).sup.1/2 }=t (11)

Therefore, the following 6 simultaneous equations are derived, in which6 unknown factors (x,y,z,Mx,My,Mz) are included.

    3t={(ax+dy+fz).sup.2 +(dx+dy+cz).sup.2 +(fx+ey+cz).sup.2 }.sup.1/2(12)

    ar.sup.7 =3x(3r.sup.2 -5x.sup.2)Mx+3y(r.sup.2 -5x.sup.2)My+3z(r.sup.2 -5x.sup.2)Mz                                              (13)

    br.sup.7 =3x(r.sup.2 =5y.sup.2)Mx+3y(3r.sup.2 =5x.sup.2)My+3z(r.sup.2 -5y.sup.2)Mz                                              (14)

    dr.sup.7 =3y(r.sup.2 -5x.sup.2)Mx+3x(r.sup.2 -5y.sup.2)My-15 xyz Mz (15)

    er.sup.7 =-15xyzMx+3z(r.sup.2 -5y.sup.2)My-15xyz Mz        (16)

    fr.sup.7 =3z(r.sup.2 -5x.sup.2)Mx-15xyzMy+3x(r.sup.2 -5z.sup.2)Mz (17)

By solving the foregoing simultaneous equations, each component of themagnetic moment and the coordinates of the point P(x,y,z) of themagnetic body may be determined.

To measure the magnetic field by only 3 points A,B and C, as shown inFIG. 2, the 3 components of the magnetic field Hx, Hy, Hz at points Aand B, respectively, and the 2 components of the magnetic field Hy, Hzat point C are measured.

Then: ##EQU10##

In case of a 3 point measurement, the solutions are obtained byreplacing b' for b, and e' for e in the previous equation (10). In thiscase, the error increases slightly within a tolerable range. Thecalculation method by the measuring data:

Since these values a,b,c,d,c,f and t can be obtained by the magneticfield measurements, they are known values. Therefore, the previouslydescribed 6 unknown values (x,y,z,Mx,My,Mz) may be determined bysolution of the equations (12)-(17).

The magnetic moments are calculated by solution of equations (15) (16)(17) as follows: ##EQU11##

The total magnetic moment is obtained by the following equation.##EQU12##

Let ##EQU13##

Then, from (13)-(14) ##EQU14##

Applying (21) to (22), ##EQU15##

From (12),

    Z=3t[{(ak+d)q+f}.sup.2 +{(dk+b)q+e}.sup.2 +{(fk+e)q+c}].sup.-1/2(24)

From (13)-(14),

    (ek-f)(k.sup.2 -l)q.sup.3 -d(k.sup.2 +l)-3(a+b)k q.sup.2 +2(ek+f)q-2d=0 (25)

Applying (23) to (25), ##EQU16##

Thus, a solution to this 6 degree equation relating to k is obtained byapplying the following calculation method.

From (26),

    f(k)=k.sup.6 +A.sub.1 k.sup.5 +A.sub.2 k.sup.4 +A.sub.3 k.sup.3 +A.sub.4 k.sup.2 +A.sub.5 k+A.sub.6 =0                             (27)

    f(k)=(k.sup.2 +Pk+Q)(k.sup.4 +B.sub.1 k.sup.3 +B.sub.2 k.sup.2 +B.sub.3 k+B.sub.4)+Rk+S=0                                         (28)

    k.sup.6 +(B.sub.1 +P)k.sup.5 +(B.sub.2 +PB.sub.1 +Q)k.sup.4 +

    (B.sub.3 +PB.sub.2 +QB.sub.1)k.sup.3 +(B.sub.4 +PB.sub.3 +QB.sub.2)k.sup.2+

    (R+BP.sub.4 +QB.sub.3)k+S+QB.sub.4 =0                      (29)

If the values of the P and Q are obtained by setting R=0, S=0 inequation (29), then the following equation provides the solution.

    k.sup.2 +Pk+Q=0

Generalizing the equation (29), the following formulae are obtained:

    R=B.sub.n-1 =0                                             (30)

    S=B.sub.n +PB.sub.n-1 =0                                   (31)

Since Bn is the function of P and Q, partially differentiate (30) and(31) by P and Q; ##EQU17## The partial derivative of B_(n) is calculatedas follows: Generalizing and comparing (27) with (29);

    B.sub.n =A.sub.n -PB.sub.n-1 -QB.sub.n-2                   (34)

where, n=1,2,3,4,5,6.

    B.sub.0 =1, B.sub.-1 =0

By partially differentiating (34) by P and Q;

    C.sub.n =B.sub.n -PC.sub.n-1 -QC.sub.n-2                   (35)

where, n=1,2,3,4,5. ##EQU18## where, n=1,2,3,4,5,6.

From (32), (33);

    C.sub.n-2 ΔP+C.sub.n-3 ΔQ=B.sub.n-1            (37)

    (C.sub.n-1 -B.sub.n-1)ΔP+C.sub.n-2 ΔQ=B.sub.n  (38)

From these equations, ΔP and ΔQ is obtained, by letting n=6, ##EQU19##Thus, B₅, B₆, C₃, C₄, C₅ is obtained by the following procedure.##EQU20##

A_(n) can be calculated from (26), B_(n) from A_(n) and C_(n) fromB_(n).

First, by assigning certain values to P and Q, respectively, ΔP and ΔQare calculating by using (39) and (40). The values of P and Q are thenreplaced by (P+ΔP)→P,(Q+ΔQ)→Q and the procedure repeated until ΔP<0.001,ΔQ<0.01, corresponding to R→O and S→O. These values of P and Q result inthe following solution.

    k.sup.2 +Pk+Q=0                                            (41)

The solution should be real numbers which are represented as follows:##EQU21##

All values of k except for the above solutions (42) are eliminatedbecause they are imaginary solutions mathematically.

From (23); ##EQU22##

The coordinates of the measuring point are obtained from these values asshown in following equations. ##EQU23##

The values of magnetic moments of the magnetic source are obtained byfollowing equations. From (19); ##EQU24##

From (20); ##EQU25##

From (19); ##EQU26##

From (20); ##EQU27##

The real solutions of the 6 degree equation, are selected and theimaginal solutions are omitted. The value of z is then determinednaturally plus or minus on a continuous curve by observing, whether themeasuring point is located above or below from the magnetic body so thatthe solution is finally reduced to only one.

ONE CONCRETE EXAMPLE

(1) Installation on Aircraft.

An example of the magnetic detection system installed in aircraft tolocate a submarine in the water, is shown in FIGS. 3 and 4.

A pair of 3 axes sensors (H_(Ax), H_(Ay), H_(Az) ; H_(Bx), H_(by),H_(Bz)) are positioned at the tip A and the tail B of the aircraft body,and a pair of 2 axes sensors (_(Cy), H_(Cz) ; H_(Dy), H_(Dz)) arepositioned at the end of wing C and D. The 3 axes sensors and the 2 axessensors form magnetometer units 10, 12, 14 and 16 through whichdirectional components of a target magnetic field at the locations ofthe units are simultaneously measured along three or two orthogonaldirections designated as X, Y and Z axes. Such magnetometer units areper se well known in the art hereinafter referred to and are operativeto produce output signals designated herein as H_(Ax), H_(Ay), H_(Az),for example, at point A as indicated with respect to unit 10 in FIG. 4.The center line of the aircraft body is located on x axis and both wingsare aligned with axis.

Assuming that the aircraft is flying on a north or south heading and inthe level flight, the output of each sensor is fed to the signalprocessing device SP, wherein x and y components of signal aremultiplied by the sine or cosine of the direction coefficient, so as tocompensate for each component of the magnetic field with respect tonorth-south and east-west when the direction of the aircraft varies.

In FIG. 3, the longitudinal center line of the aircraft body is thex-axis of each unit 10 and 12 while the y-axis of units 14 and 16extending between wing tips intersects the x-axis on a vertical linewhen the aircraft flies at the level flight whereby each sensor isarranged to avoid the effect of adjacent magnetic substances, therebyavoiding the magnetic noise. The signal is fed to the signal processingdevice SP and is calculated by computer CT and the result is sent toeach of direction indicator RI, distance indicator DI, attitudeindicator AI and magnetic moment indicator MI.

The sensor signals form analog inputs to the signal processor SP thatare digitized by well known analog to digital conversion circuits.Calculations in accordance with procedures hereinbefore described areperformed by the computer CT interfaced with the signal processorthrough appropriate data terminals. Calculated data terminals interfacethe processor SP with the indicators. The details of the computer andprocessor form no part of the present invention. Only the generalfunctions as herein described are necessary for an understanding of theinvention.

The input signal detected in sensors at points A, B, C, D are connecteddifferentially to each corresponding sensor A, B, and C, D mutually, ina manner well known in the art and the signal derivatives so obtainedwhich are then magnified. The resultant signal components therebydetected at point A for example, along the x-axis is represented by thefollowing expression:

    Δ.sub.Hx =(H.sub.Ax +H.sub.x)-(H.sub.Bx +H.sub.x)=H.sub.Ax =H.sub.Bx

where H_(x) is one component of the earth's magnetic field. Thus, theeffect of the earth's magnetic field is canceled as hereinafterexplained.

In the above arrangement, the craft body noise and the other noise areeliminated by other appropriate means, so that only the pure measuringsignal is detected and digitized without distortion applied to thecomputer CT. This signal is converted into a signal of the required formby the signal processing device SP and then the direction, distance,attitude and moment of the magnetic source are indicated and recordedcontinuously, automatically and momentarily. The computer CT preferablyhas a large memory capacity, in order to shorten the computing time.

FIG. 4 shows the block diagram of this detection system.

In this system, the magnetometer sensor is required to havedirectionality and sensitivity as well as high accuracy as high aspossible. The fluxgate type magnetometer (sensitivity: 0.1 γ/div.) whichcomprises high permeability material and the SQUID type magnetometer(sensitivity: 0.00001 γ/div.) which comprises super conductor materialare recommended at present as current commercial units for thisinvention.

The structure for 4 point measurement is shown in FIG. 5. The points A,B and C, D on the x and y axes are arranged symmetrically with respectto the measuring point P, and the 3-axes sensor units fixedly positionedat points A, B so as to be able to measure 3 orthogonal magnetic fieldH_(Ax), H_(Ay), H_(Az) ; H_(Bx), H_(By), H_(Bz) on x-axis while 2 axessensor units are fixedly positioned at the points C, D, so as to measureorthogonal magnetic field H_(Cy), H_(Cz) ; H_(Dy), H_(Dz) on y-axis. Ishow the structure of 3 points measurement in FIG. 6. The points A, B onthe x-axis are symmetrically arranged with respect to the measuringpoint P, and point C positioned on the y-axis. In this embodiment, thepoint D associated with a 4 point measurement is dispensed with.

The measuring points are on the x-y plane and each point movesintegrally as a unit and does not move independently and individually.

When the directional magnetometer sensor rotates in the uniform earthmagnetic field, it will sense the earth magnetic field and generate amuch larger signal than any other detecting signal. When the totalsensor group rotates as a unit, the earth magnetic field is compensatedfor by the differential connection of corresponding symmetrical sensorsso that only the required detecting signal is obtained. Since it isassumed that the earth magnetic field is uniform in a narrow area, evenif the sensor axis rotates, the orthogonal 3 directional resultantmagnetic field will not change, and is held constant.

It is necessary to design the sensor distance Δx and Δy to be of themost optimum value in accordance with the detection purpose,magnetometer sensitivity, the size of target magnetic body, magneticmoment and its detecting distance. The detecting distance will benaturally determined by the relation between the largeness of the targetmagnetic body and its magnetic moment and the magnetometer sensorsensitivity. The detection distance will be larger, if the sensitivityis more higher. If the distance Δx, Δy is very small, the difference inthe magnetic field becomes smaller, so that ultimately the fieldgradients cannot be determined. If the distance Δx, Δy is very large,the error becomes large, so the position of the magnetic-body cannot beprecisely determined. There is therefore an optimum distance of Δx, Δyfrom the target body. Since deviations in the perpendicularity betweensensor lines AB and CD, and the rectangularity in each sensor at eachpoint cause the error, the accurate orthogonarity of each of the sensorsis required to be as high grade as possible.

(2) Experiment on a magnetic model of a ship:

The following is an example in which a magnetic model of a ship is usedfor the measurement using the above system:

The heading of the magnetic model of the ship (total length: 180 cm,max. width: 25.3 cm, weight: 24.2 kg), constructed of steel material isnorth-south and east-west directions, and the model is shiftedhorizontally on the line in north-south direction. At that time, thedownwardly directed vertical distance is changed from model center tothe 3 axial magnetometer sensor of fluxgate type and definitely fix thesame in order to measure the 3 axial magnetic field components directeddownwardly in each plane perpendicular parallel to each axis under themodel and the equi-magnetic field curve is recorded. The total field andfield gradients of the points on the N-S line in the positions of thesensor just vertically under the model, spaced a certain distance frommodel line in eastern and western direction, are computed and data soobtained is introduced into the theoretical equations and the measuringpoint and the center of magnetic model of the ship are carried out bymeans of computer. At that time, the distance between sensors wasdetermined by simulating the actual airplane installation as follows:

    x=72 cm, y=75 cm.

The results of this experiment were as follows:

A comparison was made between the true value of the distance between themeasuring point and the center point of the magnetic model of the shipcomputed by the coordinate x,y,z and the value of distance computed bythe magnetic field measurement based on this method.

FIGS. 7, 8 and 9 show the comparison of the true distance with thedistance computed by this method about each point on the north-southline through 3 points; i.e., the points at vertical distance 150 cm fromthe center of the model, and at distance 150 cm shifted in easterndirection and at distance 150 cm shifted in western direction bydirecting the model to east and west heading. These values coincidesubstantially with each other, as shown in these figures.

Various causes of the distance error, apparently occur, such as: Errorcaused by the experiment, error by putting nearly equal measuredmagnetic field instead of theoretical equation, error by replacing acertain actual magnetic source by point magnetic dipole, etc. However,the errors based on these causes will be almost negligible when thedistance of the measuring point from the object is more than 1.5 timesthe total length of the magnetic source. The error caused by theexperiment is substantial.

Therefore, the method of this invention is for high accurate detectionof the position of magnetic source, provided that the satisfactory totalfield and field gradients can be measured as explained herein by thedetection theory.

(3) Applicable field of this invention

The target substances which can be detected by the method of thisinvention and the features of this method of invention are as follows:

(1) Target substances to be detected.

(a) All substances which are constructed with steel materials:

Ship's body, Tank, Armored vehicle, Motor car, Steel cases, Mine cases,Non-explosive Bomb, Rifle and Gun, pistol, swords, cans and a smallmagnetic body assembly, etc.

(b) All embedded mineral ore having magnetism: Underground mineral ore,underwater oil field, embedded magnetic materials in Satelite, etc.

(2) Features of this invention.

(a) The target substances can be necessarily detected, if they havemagnetic materials, even if it is impossible to detect them by the nakedeyes, light, electro-magnetic wave, ultra sonic wave, infrared rays andother physical phenomena.

(b) Even if the target substance and measuring point are at rest or aremoving, the relative position between target and measuring point can bedetected continuously time to time.

(c) The position of the target magnetic body can be detected, recordedand displayed without time lag as a point by means of the magneticfield.

(4) Fields to which this invention is applicable.

(A) General commercial industry

(a) The detection of embedded mineral ore and magnetic substances underthe bottom of sea and underground.

(b) The detection of unexplosive bombs and mines and other steelstructures embedded in the bottom sand or mud, during the dredgingoperation at the entrance of port and bay or the narrow water path.

(c) The detection of embedded pistols and swords, etc. in the river orpool, in case of criminal search.

(d) The archaeological detection of the swords and iron made vesselswhich are excavated in the acient ruins in Persia, Egypt, Peru, etc.

(e) The detection of the position of sunken ships in salvage.

(f) The detection of position of embedded magnetic materials bysatellites passing near the planets

(B) Defense industry.

(a) This is the most effective technique to detect a submergedsubmarine, from an anti-submarine aircraft.

(b) This is a necessary technique to search and detect the location ofmines laying at the bottom of the sea and embedded mines under sand, mudand algae in the sea.

(c) The automatic detection of the position of Tanks, Armored vehiclesand Motor cars, etc.

(d) The detection of the position of an approaching ship, when layingmines in the deep sea.

I claim:
 1. A method of detecting the position of a magnetic sourcerelative to a measuring point (P) and associated magnetic moments bymeasuring total source generated field strength and field strengthgradients at said measuring point, including the steps of: establishingtwo measuring locations (A and B) symmetrically displaced from themeasuring point along a first axis (X); establishing at least a thirdmeasuring location (C) displaced from the measuring point along a secondaxis (Y) perpendicular to and intersecting the first axis at themeasuring point; mesuring three directional components of the fieldstrength (H_(Ax), H_(Ay), H_(Az) ; H_(Bx), H_(By), H_(Bz)) at each ofsaid two measuring locations defined by the intersection of the firstaxis and two other mutually perpendicular intersecting axes respectivelyparallel to the second axis and a third axis (Z); and measuring twodirectional components of the field strength (H_(Cy), C_(Cz)) at saidthird measuring location along the second axis and a perpendicularintersecting axis parallel to the third axis.
 2. The method of claim 1including the step of: establishing a fourth measuring location (D)displaced from the measuring point along said second axis in symmetricalrelation to the third measuring location; and measuring two directionalcomponents of the field strength (H_(Dy), H_(Dz)) at said fourthmeasuring location along the second axis and a perpendicularintersecting axis parallel to the third axis.
 3. The method of claim 2wherein said measurements of the directional components of the fieldstrength are respectively effected by generation of correspondingsignals at each of the measuring locations, the signals generated at themeasuring locations symmetrically displaced from the measuring pointbeing subtracted from each other to cancel the influence of the earth'smagnetic field on the measurements.
 4. The method of claim 2 includingthe step of: correcting said measurements of field strength componentsfor magnetic azimuth angle deviations.
 5. The method of claim 2 whereinsaid mesurements of the directional components of the field strength arerespectively effected by generation of corresponding signals at each ofthe measuring locations, the signals generated at the measuringlocations symmetrically displaced from the measuring point beingsubtracted from each other to cancel the influence of the earth'smagnetic field on the measurements.